Will and Kathy has some money each. If Kathy gives Will $15, he will have 7 times as much money as her. If Will gives Kathy $13, he will have the same amount of money as her. How much money does each person have respectively?
- Will?
- Kathy?
| |
Case 1 |
Case 2 |
| |
Will |
Kathy |
Will |
Kathy |
| Before |
7 u - 15 |
1 u + 15 |
4 u + 13 |
4 u - 13 |
| Change |
+ 15 |
- 15 |
- 13 |
+ 13 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Kathy gives Will some money or Will gives Kathy some money, the total amount of money remains the same.
Total amount that Will and Kathy have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Will and Kathy each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Will has at first in Case 1 and Case 2 is the same.
7 u - 15 = 4 u + 13
7 u - 4 u = 13 + 15
1 u = 28
Amount that Will has
= 4 u + 13
= 4 x 28 + 13
= 112 + 13
= $125
(b)
Amount that Kathy has
= 1 u + 15
= 28 + 15
= $43
Answer(s): (a) $125; (b) $43
